Comparison of methyl rotation axis order parameters derived from model-free analyses of H-2 and C-13 longitudinal and transverse relaxation rates measured in the same protein sample

Recombinant HIV-1 protease was obtained from bacteria grown on a 98% D2O me dium containing 3-C-13 pyruvic acid as the sole source of C-13 and H-1, The purified protein is highly deuterated at non-methyl carbons, but contains significant populations of (CHD2)-C-13 and (CH2D)-C-13 methyl isotopomers. This pattern of isotope labeling permitted measurements of H-1 and C-13 rel axation rates of (CHD2)-C-13 isotopomers and H-2 (D) relaxation rates of (C H2D)-C-13 isotopomers using a single sample. The order parameters S-axis(2) , which characterize the motions of the methyl rotation axes, were derived from model-free analyses of R-1 and R-2 data sets measured for C-13 and H-2 spins. Our primary goal was to compare the S-axis(2) values derived from t he two independent types of data sets to test our understanding of the rela xation mechanisms involved. However, S-axis(2) values derived from the anal yses depend strongly on the geometry of the methyl group, the sizes of the quadrupolar and dipolar couplings, and the effects of bond vibrations and l ibrations on these couplings. Therefore uncertainties in these basic physic al parameters complicate comparison of the order parameters. This problem w as circumvented by using an experimental relationship, between the methyl q uadrupolar, C-13-C-13 and C-13-H-1 dipolar couplings, derived from independ ent measurements of residual static couplings of weakly aligned proteins by Ottiger and Bar (J. Am. Chem. Soc. 1999, 121, 4690-4695) and Mittermaier a nd Kay (J. Am. Chem. Sec. 1999, 121, 10608-10613). This approach placed a t ight experimental restraint on the values of the H-2 quadrupolar and C-13-H -1 dipolar interactions and greatly facilitated the accurate comparison of the relative values of the order parameters. When applied to our data this approach yielded satisfactory agreement between the S-axis(2) values derive d from the C-13 and H-2 data sets.